Gaining New Perspectives

By Aristotle Ou posted 25 days ago


To build empathy

Follow their thinking, not yours

Be patient, listen

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Examine the dot card above (You may recognize this from Jo Boaler’s Week of Inspirational Math activities). How many dots do you see? How did you count them? Did you see the arrangement of five dots found on the face of a six-sided die with one additional dot on the left and right side? Did you see the outer six dots forming a hexagon with one dot in the middle? What does this activity teach us about how we think?

Dot talks, along with number talks and pattern talks, demonstrate how students see and engage with images, words, and ideas differently. These routines also help students develop and understand alternative ways of thinking. When students keep an open mind, listen to each other’s ideas, and try to understand the thinking of others, they gain a new perspective on the subject and improve their learning. Empathizing and approaching a problem from the perspective of all teammates leads to a stronger cooperative learning environment. To build empathy and an appreciation for other perspectives, I have students analyze, assess, and reflect on their peers’ thinking or learning after activities that explore multiple approaches and solutions.

One activity that allows for understanding different perspectives is College Preparatory Mathematics’ task on multiple representations of quadratic patterns. I schedule three and a half days for teams to investigate their assigned pattern, create a stand-alone poster to represent their group’s solution, engage in a gallery walk, provide feedback in the form of two stars and a wish on post-it notes, debrief on the gallery walk, analyze feedback from their peers, and debrief on the feedback. I coordinate with our amazing Library Media Technician, Laura Schwoerer (@librarynoise), to display the posters and hold the gallery walk in the school library, so students can analyze the posters in a large space and provide feedback to students in all four of my classes.

Immediately after the gallery walk, I ask my students to reflect on the patterns they notice in all the posters. Students shared how too many colors or too much white out distracted from understanding a team’s solution. Students also noted how a lack of explanation of how a team saw their pattern or found their rule made their work more confusing. The following day, I passed back the feedback left on the posters. After analyzing and reading through the post-its, I asked teams to share any constructive feedback. In every class, only a couple of post-its were read, so I asked them to think about the feedback they left for other groups. After acknowledging only a handful of post-its with constructive feedback, I wanted students to think about how their feedback may have been perceived by other groups.

Another way I help my students develop empathy is by having them guide their peers’ learning in preparation for a reassessment I give at the end of each semester. As peer tutors, students spend a couple of days helping each other understand concepts by going through practice problems, asking questions, or reteaching a lesson. By checking their peers for understanding, peer tutors try to understand and follow their peers’ thinking. After the activity, I ask the following questions to help students reflect on their peers’ learning.

  • What did you do to help your classmates grow as mathematicians (did you ask questions, reteach a lesson, etc.)?
  • What did you find was most successful in helping your peers understand the concepts?
  • What was the most challenging part of helping your peer(s)?
  • Based on your observations of your peers’ learning, what would you do differently as a teammate in future groups?

Students limit their learning when they neglect to see a math problem from another student’s perspective. Cultivating a classroom of empathetic learners maximizes the learning opportunities for all students.

#MiddleSchool #blog #learn #reflection

Beyond your approach

Behind the lens of others

Lies new connections